Bounded confidence model on growing populations

Abstract

This paper studies the bounded confidence model on growing fully-mixed populations. In this model, in addition to the usual opinion clusters, significant secondary clusters of smaller size appear systematically, while those secondary clusters appear erratically and include much fewer agents when the population is fixed. Through simulations, we derive the bifurcation diagram of the growing population model and compare it to the diagram obtained with an evolving probability density instead of agents, and with their equivalent with a fixed population. Our tests when changing the usual bounded confidence function into a smooth bounded confidence function suggest that these secondary clusters are mainly generated by a different mechanism when the population is growing than when it is fixed.